Inflation, a period of accelerated expansion at the beginning of the Universe, seeks to explain the (otherwise mysterious) large scale smoothness, isotropy, and “oldness” of the Universe. An important product of this inflationary epoch is the origin of density perturbations that are the seeds of galaxies and other large structures today. The density perturbations and gravitational waves produced by inflation provide sensitive tests of both the inflationary paradigm and of individual inflationary models. In the past decade predictions of inflation have been tested by Cosmic Microwave Background data, most recently with the Planck satellite observations. The basic idea of inflation matches the data and sensitive tests have been made of individual models. Planck data have ruled out most inflation models. I will discuss the status of Natural Inflation, a model that my collaborators and I originally proposed in 1990, as well as modern variants. Natural inflation uses “axions” as the inflaton, where the term “axion” is used generically for a field with a flat potential as a result of a shift symmetry. The successes of inflation as well as the potential discoveries in upcoming data will be emphasized.